Yes. It should. However I do not know if the band 71 is Firmware dependent. I am trying to see a way to view the LTE bands on mine to help out. The main thing to know is the Factory unlocked model has the same FCC ID as the carrier variants (A3LSMG965U). The FCC ID should be tied to the type of Hardware or radios and so like the S8/S8+ they have one type for multiple models carrying the Snapdragon processor.
It falls under a different label under the same FCC ID. The software onboard and bloatware is less. However if you want T-Mobile VVM or the T-Mobile software preinstalled it won't come on the SMG965U1 factory unlocked model.
Yeah as far as I know all the US models have same hardware including the same bands. It's just they run different firmware based on the carrier or unlocked.